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Lesson Plan #36A http://www.phy6.org/stargaze/Lsun1litA.htm

(S-1A) &nbsp Weather and the Atmosphere

A mostly qualitative discussion of the way vertical convection transports heat from the surface upwards, and the associated pressure and temperature profiles of the atmosphere. The role of humidity in forming clouds, in particular thunderstorms.

Part of a high school course on astronomy, Newtonian mechanics and spaceflight
by David P. Stern

Goals: These sections are qualitative, but they cover a wide range of phenomena. They contain material which can cover more than one session, and the teacher can choose what is to be included and what is left out.

The student will learn

About the distribution of density, pressure and temperature in the atmosphere. With increasing altitude, pressure decreases, because it is proportional to the weight of air above the observation point. Density decreases in proportion to pressure, dropping by about 1/2 with each 5 kilometers of altitude.

The main vertical motions in the atmosphere are the rising of air warmed at the ground (heated by sunlight) and the descent of air which has radiated its heat to space.
This circulating flow is known as convection. Since rising air cools as it expands, the temperature drops with altitude.

Convection and the cooling associated with it take place in the troposphere, the layer where weather occurs. It ends at the tropopause, at about 10-16 km (higher in the tropics). Above it is the stratosphere where temperature is first constant (about –55° C) and then increases because of absorption of ultra-violet sunlight by ozone, typically at 25-40 kilometers.

The student will learn that heat originating in sunlight is stored by the atmosphere in two forms: as a rise in temperature and as humidity, evaporated water dissolved in air (turning water into vapor absorbs energy).

Humidity has a limit, depending on the temperature of the air. As air cools, that limit drops and ultimately water is forced out, to form clouds (little droplets) and rain (big drops). The energy is returned to the air, which then warms up.

The warming of air by releasing humidity is particularly intense in thunderstorms, where a rapidly rising column of humid air ("thunderstorm cell") extends from near the ground to the base of the stratosphere.

Milder but more widespread rising currents occur over land on hot summer days, ending in small fleecy clouds at typical altitudes of 1 km.

Stories: The quote "Everyone talks about the weather but no one does anything about it" (not from Mark Twain but from his friend Charles Dudley Warner).

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Starting the lesson:

Humans--and other land creatures--are a bit like fish--their lives depend on the ocean of water, in which they swim, while our lives depend on our ocean of air, the atmosphere.

The watery ocean ends abruptly--it has a well defined top, separating the water below from the air above. Our atmosphere also has a limited extent, and above it is near-empty space. But its upper boundary is not like that of the ocean. What is the difference?

Unlike the sudden transition from water to air, the transition from air to space is very gradual.

(Explain)
Water in the ocean, at all levels, has about the same density--about 1 gram per cubic centimeter, or a tiny bit more because of the salt dissolved in it. That is the behavior you find in liquids. At the bottom of the ocean, water is under enormous pressure, from the weight of all the water above it, but this hardly changes its density.

Air is a , so its density depends on the pressure which confines it. That pressure comes from the weight of all the air above it. At sea level, that is about as much weight as 10 meters of water, or 32 feet of water. As you rise in the atmosphere, some of that air is now below you, so the pressure is less, and the air gets more rarefied.

So--at what height do you think space begins?
(let students express opinions)

&nbsp There is no single answer! It all depends on your definition of "space." Gravity may hold on individual atoms up to about 5 Earth radii--about 32,000 kilometers, since one radius is 6371 km. Electrically charged ions and electrons are held magnetically about 3 times as far--it also depends on direction, and on the "solar wind" of ions and electrons streaming from the Sun, which limits the spread of the magnetic influence of the Earth.

But for practical purposes, we will take about 100 kilometers.

That, by the way, was the boundary defined by the "Ansari X-prize" which in 2004 awarded $10,000,000 to the first privately built manned spacecraft, able to carry 3 humans to 100 kilometers, land safely and repeat the feat within 2 weeks. The prize was won in October 2004 by "SpaceShipOne" designed by Burt Rutan (you can find more about it on the web).

But there exists a physical reason, too. Above that altitude, air is so rarefied, that many molecules reaching that altitude while moving upwards continue moving with no more collisions, until gravity pulls them down again, like tossed stones.

Up to this level, collisions are frequent, so that the atmosphere remains "well mixed" at the familiar ratio--about 21% oxygen. All molecules share the same average kinetic energy (1/2)mv2, which depends on the local temperature.

However, because they have different mass, equal energy means different velocities! Lighter molecules move faster and rise higher, so above about 100 kilometers (the "thermopause", if you need a word for it), the composition of the atmosphere changes. Oxygen molecules are a bit heavier, so nitrogen should rise higher. But in fact, sunlight breaks up many oxygen molecules to individual atoms, and those rise higher and dominate the composition of a good part of the fringes of the atmosphere.

[As a curiosity, one can note that when one goes really far--say, 1 Earth radius, about 6000 km (or 4000 miles), most of the few remaining atoms are hydrogen which, being the lightest substance, have the greatest velocity and rise highest.

The amount of hydrogen involved is tiny--there isn't much of it in the atmosphere to begin with, it might come from break-up of water vapor by sunlight. But the hydrogen cloud surrounding Earth--known as the geocorona has some interesting interactions with sunlight and with trapped ions of the radiation belt, and has been
photographed from the Moon.

How high does one have to go, for the density to drop to 1/2?
(let students guess)

&nbsp About 5 kilometers, in the lower atmosphere. At this altitude, half the mass of the atmosphere is below you, half is above. Therefore the weight compressing the air is only half of what it is near sea level, and by Boyle's law, the density of a gas is proportional to the pressure that keeps it confined.
So the density is one half too.

Suppose you go up another 5 kilometers--to 10 kilometers, the height at which jetliners fly. What do you think is the density there?

&nbsp Half of what it is at 5 kilometers, that is, 1/4 of the sea-level pressure. If the temperature of air were constant, it would decrease by half about every 5 kilometers. Actually, the "halving distance" varies somewhat with heaight, because it also depends on temperature.

[Optional: You may see in books the term "scale height. That is the height over which the density decreases by a factor 2.71828..., it comes to about 8 kilometers or 5 miles. The number 2.71828..., commonly denoted by the lower-case letter e, arises naturally in many calculations, e.g. the cooling rate of a hot object, or the unrestricted multiplication of bacteria.]

If the "halving height" were a constant 5 kilometers, what would be the density at 100 kilometers? (Use calculator)

&nbsp That is 20 "halving heights", so the density is reduced 220 times, or about a million times smaller than at sea level.

What is atmospheric convection and what causes it?

&nbsp Convection is the vertical circulation of air--warm air. Heated by the ground, rises , gets rid of its heat higher up in the atmosphere by radiating it to space, then--being denser and heavier than surrounding air, which still has its heat--flows down again.

A 3rd grade teacher once wrote about being stumped by a student asking "why is it so cold high up? If it's hot air that rises, high up air should be hot, air near the ground, cold. How would you answer this?

&nbsp One could answer "air is indeed heated near the ground, but as it rises, air pressure drops and any expanding gas cools down."

[Optional: That is how an air conditioner works! The gas inside flows outside the house, where an electric compressor compresses it, which heats it up. It then returns to the house, where it is allowed to expand again.

If the gas were just allowed to expand, it would cool back to its first temperature. However, before flowing back to the house, it flows through an array of pipes and fins ("radiator") on which a fan is blowing air, and that pre-cools it. Therefore, when it finally expands inside the house, it is colder than before, and it can absorb heat from the house and condense water vapor, on another "radiator" inside the building.]

[Optional] The rate at which temperature drops with height is called the lapse rate. In dry air, it is as high as 1°C per 100 meters. In very humid air it is 0.6°C, and in practice it is typically 0.65°C

See also here.
One of many internet references is http://www.uwsp.edu/geo/faculty/ritter/geog101/textbook/atmospheric_moisture/lapse_rates_1.html

Warm air can hold much more water than cold air. So--
how do you think clouds form?

&nbsp Rising humid air cools to where it cannot hold all its water vapor. Some is squeezed out to form little droplets, and those make up the clouds.

(If someone asks "why doesn't gravity make the clouds fall down" point out that tiny droplets fall very, very slowly, and meanwhile there may be a rising flow from below, pushing them up. In fact, on a warm humid summer day, the clouds actually grow taller and taller because of that push.)

What produces a thunderstorm?

&nbsp Thunderstorms often occur in very warm and very humid air. Convection gets very powerful, forming a "thunderstorm cell", an updraft reaching from near the ground to the tropopause, the cold level from which air can radiates directly to space. The flow is so fast and intense, that water forms not just little droplets, but big raindrops.

A thunderstorm often drops hail. How does it happen?

&nbsp The upwards flow of air in the thunderstorm cell is so fast that it overcomes gravity and sucks raindrops upwards, into a colder environment, where they freeze.

[Freezing actually releases more heat and helps the flow rise even more!]

When a thunderstorm approaches, you suddenly note a sudden wind. Any guess what causes it?

&nbsp Probably air sucked into the thunderstorm.

Note: Often thunderstorms appear in a group, in what is known as squall line. The thunderstorms and the larger weather system sometimes cause the air to rotate, and this rotation speeds up greatly as the air is sucked inwards, towards the main cell. This is how a tornado is produced.

Thunderstorms also produce lightning. This subject is beyond the scope of this discussion, but more can be found here.

On a hot summer day, small white clouds form over the land. If you fly a glider or small plane below them as you come under a cloud you suddenly feel you are being lifted. Why:

Your plane is being lifted by the rising column of warm air which has created the cloud.

...and once you get out of the updraft, it seems as if you drop down again. That moment can be hard on the stomach of many passengers!